A prosthesis of this kind is shown in the patent application WO 97/25943. A bearing body connectable to a shaft in the upper arm has, at its lower side, a projecting cone with a circular cross-section and index bores for a pin projecting out of the shaft to fix the bearing body with its circular cone in different angular positions. With this arrangement, the index bores and the projecting pin must have a minimum clearance relative to one another so that the cone and the counter surface reliably form a connection. Due to this clearance, torsional forces are also transmitted at the connection which can only be transmitted by the static friction and which occur in addition to the axial loads at the friction points. Such a frictional connection is more at risk as a connection by the additionally occurring shear stresses through torsional loading, with a spread of the transmittable forces already arising from the blow by which a press-fit has to be produced and from the condition at the cone surfaces.